Enter the total number of objects and the sample size to calculate the number of possible permutations.
How to Calculate Permutations
Permutations are used to calculate the number of ways to arrange a set of objects in a specific order. This is a fundamental concept in combinatorics and probability theory.
Permutations Formula
The formula for calculating permutations is:
\[P(n,r) = \frac{n!}{(n-r)!}\]
Where:
n is the total number of objects
r is the number of objects being arranged
P(n,r) is the number of permutations
! denotes factorial
Calculation Steps
Identify the total number of objects (n) and the sample size (r).
Calculate n! (n factorial).
Calculate (n-r)! ((n-r) factorial).
Divide n! by (n-r)! to get the number of permutations.
Example
Let's calculate the number of permutations for arranging 5 books on a shelf if we only have space for 3 books.
n = 5 (total number of books), r = 3 (number of books to arrange)
Calculate 5!:
5! = 5 × 4 × 3 × 2 × 1 = 120
Calculate (5-3)! = 2!:
2! = 2 × 1 = 2
Apply the formula:
\[P(5,3) = \frac{5!}{(5-3)!} = \frac{120}{2} = 60\]
Visual Representation
This diagram illustrates the permutation calculation for our example. It shows that there are 60 ways to arrange 3 books out of 5 on a shelf.